29.15.3 problem 411

Internal problem ID [5009]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 15
Problem number : 411
Date solved : Monday, January 27, 2025 at 10:03:06 AM
CAS classification : [_separable]

\begin{align*} \left (1-4 \cos \left (x \right )^{2}\right ) y^{\prime }&=\tan \left (x \right ) \left (1+4 \cos \left (x \right )^{2}\right ) y \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

dsolve((1-4*cos(x)^2)*diff(y(x),x) = tan(x)*(1+4*cos(x)^2)*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \left (4 \cos \left (x \right )-\sec \left (x \right )\right ) c_{1} \]

✓ Solution by Mathematica

Time used: 0.413 (sec). Leaf size: 23

DSolve[(1-4 Cos[x]^2)D[y[x],x]==Tan[x](1+4 Cos[x]^2)y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 (2 \cos (2 x)+1) \sec (x) \\ y(x)\to 0 \\ \end{align*}